CN103425815B - Analogy method for high polymer material - Google Patents
Analogy method for high polymer material Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 31
- 239000002861 polymer material Substances 0.000 title claims abstract description 20
- 239000000945 filler Substances 0.000 claims abstract description 177
- 239000002245 particle Substances 0.000 claims abstract description 170
- 229920000642 polymer Polymers 0.000 claims abstract description 45
- 238000006073 displacement reaction Methods 0.000 claims abstract description 30
- 238000000329 molecular dynamics simulation Methods 0.000 claims abstract description 19
- 238000004364 calculation method Methods 0.000 claims abstract description 14
- 238000005381 potential energy Methods 0.000 claims description 62
- 239000011324 bead Substances 0.000 claims description 13
- 238000009792 diffusion process Methods 0.000 claims description 6
- 238000011156 evaluation Methods 0.000 claims description 2
- 238000004088 simulation Methods 0.000 abstract description 11
- 230000000052 comparative effect Effects 0.000 description 9
- 238000010586 diagram Methods 0.000 description 5
- 229920001971 elastomer Polymers 0.000 description 5
- 239000008187 granular material Substances 0.000 description 5
- 238000012986 modification Methods 0.000 description 5
- 230000004048 modification Effects 0.000 description 5
- 239000005060 rubber Substances 0.000 description 4
- 239000006229 carbon black Substances 0.000 description 3
- 230000005484 gravity Effects 0.000 description 3
- 239000000463 material Substances 0.000 description 3
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 2
- 238000005034 decoration Methods 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 239000003153 chemical reaction reagent Substances 0.000 description 1
- 150000001875 compounds Chemical class 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000000806 elastomer Substances 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- TWNQGVIAIRXVLR-UHFFFAOYSA-N oxo(oxoalumanyloxy)alumane Chemical compound O=[Al]O[Al]=O TWNQGVIAIRXVLR-UHFFFAOYSA-N 0.000 description 1
- VDGJOQCBCPGFFD-UHFFFAOYSA-N oxygen(2-) silicon(4+) titanium(4+) Chemical compound [Si+4].[O-2].[O-2].[Ti+4] VDGJOQCBCPGFFD-UHFFFAOYSA-N 0.000 description 1
- 239000008188 pellet Substances 0.000 description 1
- 230000008447 perception Effects 0.000 description 1
- 230000003334 potential effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 229920005989 resin Polymers 0.000 description 1
- 239000011347 resin Substances 0.000 description 1
- 239000000377 silicon dioxide Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
- G16C20/30—Prediction of properties of chemical compounds, compositions or mixtures
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L21/00—Compositions of unspecified rubbers
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L2666/00—Composition of polymers characterized by a further compound in the blend, being organic macromolecular compounds, natural resins, waxes or and bituminous materials, non-macromolecular organic substances, inorganic substances or characterized by their function in the composition
- C08L2666/02—Organic macromolecular compounds, natural resins, waxes or and bituminous materials
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
- G01N33/44—Resins; Plastics; Rubber; Leather
- G01N33/445—Rubber
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
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- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- Crystallography & Structural Chemistry (AREA)
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- Bioinformatics & Computational Biology (AREA)
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Abstract
Disclose a kind of computerization analogy method for being used to assess that filler is scattered in high polymer material.This method includes：Simulation steps, in simulation steps, by using the filler model and polymer mold being placed in predetermined Virtual Space, carry out Molecular Dynamics Calculation；Appraisal procedure, in appraisal procedure, according to the result of simulation steps, assess the scattered of filler model.Appraisal procedure includes：The step of calculating the most mean square displacement of the particle of force, for the particle of most force, define the maximum of filler particles and end distance.Therefore, can assess in the short period of time scattered.
Description
Technical field
The present invention relates to a kind of analogy method for high polymer material, this method can determine in the short period of time
Simulation and the deployment conditions for assessing filler in high polymer material.
Background technology
Compounded rubber of the high polymer material such as vehicle tyre, generally comprise filler such as carbon black and titanium dioxide
Silicon.The scattered performance such as intensity to rubber of filler has strong influence in compounded rubber known in the art.
In recent years, in order to assess the deployment conditions of the filler in high polymer material, it is proposed that various computerization simulations
（Numerical computations）Method.
In this analogy method, the filler model and polymer mold of filler in high polymer material are defined, and
To placing or being set in filler model and polymer mold progress molecular dynamics in predetermined Virtual Space（MD）Calculate.
Then, according to analog result, operating personnel assess the scattered of filler.Accordingly, it is difficult to provide objective and accurate assessment.
In addition, in order to simulate the scattered of filler, calculating the motion of filler model needs to spend the long period.
The content of the invention
It is therefore an object of the present invention to provide a kind of computerization mould for being used to assess that filler is scattered in high polymer material
Plan method, simulation can be determined in the shorter time by this method and assess the dispersity of filler.
According to the present invention, a kind of computerization analogy method for being used to assess that filler is scattered in high polymer material, including
Following step：
Filler model definition step, the filler model of filler defined in it, wherein each filler model represents multiple fillers
Particle；
Polymer mold definition step, the polymer mold of high polymer material defined in it, wherein each polymer in-mold
Type represents one or more polymer beads；
Simulation steps, wherein the polymer mold and filler model for being placed in predetermined Virtual Space divide
Subdynamics calculates, and
Appraisal procedure, wherein the dispersity for the outcome evaluation filler model that basis obtains from simulation steps,
Wherein
Between the particle including filler particles and polymer beads, definition cause when between the particle that be related to away from
From being reduced to a distance from predetermined cut-off（cutoff distance）Occur the potential energy to interact when following between particle,
In each filler model, a filler particles are defined as the particle of most force, to which defines maximum
End distance, and
Appraisal procedure includes wherein calculating the mean square displacement of the most particle of force（mean-square
displacement）The step of.
The method according to the invention may have following characteristics（I）-（III）：
(I) filler particles of each filler model are single centre filler particles, and at least four surface filler particles
It is centrally located on spherical surface, the center superposition of the Center-to-Center filler particles of spherical surface,
Balance length is each limited between center filler particles and surface filler particle and between surface filler particle
Degree, and
Center filler particles are the particles of most force；
(II) the cut-off distance between the filler particles of center be more than above-mentioned spherical surface radius and surface filler particle it
Between cut-off apart from sum；
(III) the step of appraisal procedure includes calculating mean square displacement at the time interval wherein more than five times.
Therefore, in filler model, come from the potential energy outside filler model, act on any other filler particles it
Before, act on most on the particle of force.In Molecular Dynamics Calculation, the particle of most force is treated as filler model
Represent a little.If the most mobile increase of the particle of force, it is believed that filler model is widely disperseed.
According to mean square displacement, the moving range of the particle of time per unit most force can be obtained.
Therefore, the scattered of filler model can be grasped, therefore the scattered of filler can be reliably assessed in the shorter time
State.
Brief description of the drawings
Fig. 1 is the perspective view of the computer system of the carry out analogy method as the specific embodiment of the invention.
Fig. 2 is the flow chart of the analogy method in this embodiment.
Fig. 3 is the schematic diagram for showing filler model.
Fig. 4 is the schematic diagram for showing polymer mold.
Fig. 5 is the schematic diagram for illustrating filler particles and polymer beads potential energy.
Fig. 6 is the schematic diagram for illustrating filler particles cut-off distance.
Fig. 7 is the perspective view for the Virtual Space that explanation is provided with filler model and polymer mold.
Fig. 8 is the schematic diagram for illustrating filler particles moving range.
Fig. 9 is the mean square displacement figure of the most particle of force.
Figure 10 is to depict the mean square displacement figure calculated by various methods.
Embodiment
Presently in connection with accompanying drawing, embodiments of the present invention are described in detail.
Analogy method according to the present invention is that one kind is used to simulate and assess in high polymer material by using computer
The scattered method of filler.
Here, term " high polymer material " refers to comprising at least rubber, resin and elastomer.
Here, term " filler " refers to comprising at least carbon black, silica and aluminum oxide.
For example as shown in figure 1, computer 1 includes fuselage 1a, keyboard 1b, mouse 1c and display 1d.Fuselage 1a includes calculating
Art processor（CPU）, ROM, working storage, storage device such as disk, disc driver 1a1 and 1a2 etc..Filled in storage
In putting, storage carries out program/software of analogy method.
Fig. 2 is the flow chart of the analogy method as the specific embodiment of the invention.
In this approach, first, it is defined the step S1 of filler model.In the step S1, as shown in figure 3,
The filler model 3 of filler is defined, wherein each filler model 3 is defined as representing multiple filler particles 4（Such as carbon black pellet）,
And filler particles 4 are the spheroids for having certain diameter.
By way of parenthesis, filler model 3 corresponds to the pass the numerical data required for molecular dynamics processing filler（Including each
Quality, volume, diameter and the initial coordinate of filler particles 4）.This numerical data is transfused to and is stored in computer 1.
The filler particles 4 for forming each filler model 3 are single centre filler particles 4c, and eight in this embodiment
In at least four surface filler particles in surface filler particle 4s, surface filler particle 4s center C is located at spherical surface B
On, spherical surface B Center-to-Center filler particles 4c center superposition.
In each filler model 3, between center filler particles 4c and surface filler particle 4s and in surface filler
Between particle 4s, there is provided the connects chain 4j of equilibrium length is each defined thereon.
Here, when the relative position of the surface filler particle 4s on spherical surface B becomes to stablize, equilibrium length is center
Bond length between filler particles 4c and surface filler particle 4s and between surface filler particle 4s.
If bond length changes, equilibrium length is returned to so as to as stable state by connects chain 4j.
In the filler model 3 of this embodiment, center filler particles 4c and surface filler particle 4s bondings（bonded）,
Keep their relative position.In addition, center filler particles 4c and the surface filler of more than three in each filler model 3
Grain 4s is arranged not to be located at identical plane or a plane.Surface filler particle 4s is located at polyhedral summit, and
Center filler particles 4c is located at polyhedral center.
Then, the polymer mold 5 of high polymer material is defined.（Step S2）
In step S2, as shown in figure 4, each polymer mold 5 is defined as representing at least one polymer beads
6, preferably multiple polymer beads 6 of high polymer material.
By way of parenthesis, polymer mold 5 corresponds to the pass the numeral money required for molecular dynamics processing high polymer material
Material.This numerical data is transfused to and is stored in computer 1.
In this embodiment, the polymer beads 6 of polymer mold 5 include the basic granules 6b of modification and without repairing
The particle 6a of decorations, and
Define the different potentials for particle 6a and particle 6b（It is mentioned below）.
Each particle 6a and 6b are the spheroids for having certain diameter.
Between particle 6a and 6b, connects chain 6j be present, to hold them under constraint, and gather with such as straight chain
The same three-dimensional structure of compound.
Then, simulated conditions setting steps S3 is carried out.
In step s3, it is provided for carrying out subsequent molecular dynamics（MD）Simulated conditions required for calculating.At this
In individual embodiment, first, potential energy definition step S3a is carried out.
In step S3a, as shown in figure 5, in filler particles 4c, 4s and another filler mould of a filler model 3
Between filler particles 4c, 4s of type 3, filler model 3 filler particles 4c, 4s and polymer mold 5 polymer beads 6a,
Between 6b, in polymer beads 6a, 6b and another polymer mold 5 of a polymer mold 5 polymer beads 6a, 6b
Between, define respective potential energy.
Stored in computer 1 using potential energy as data information, and potential energy be used to calculate two involved particles
Between power.Here, potential energy is the function of the distance between involved particle.U is calculated by following formula (1).
U=aij(1-rij/rc)2/2
Wherein
aijThe constant of potential energy U intensity being defined is corresponded between involved particle,
rijIt is the distance between center of involved particle, and
rcIt is the cut-off distance pre-defined between involved particle.
According to formula (1), if potential energy U is defined as distance rijIt is reduced to pre-defined cut-off distance rcBelow so that
Interact (in this embodiment, referring to repulsive force) generation.If distance rijMore than cut-off distance rc, then potential energy U
It is zero, and occurs without repulsive force between particles.
In this special embodiment, the combination for following two particle, potential energy U1-U10 is defined:
Particle 4c-6a:Potential energy U1
Particle 4c-6b:Potential energy U2
Particle 4c-4s:Potential energy U3
Particle 4s-6a:Potential energy U4
Particle 4s-6b:Potential energy U5
Particle 6a-6b:Potential energy U6
Particle 4c-4c:Potential energy U7
Particle 4s-4s:Potential energy U8
Particle 6a-6a:Potential energy Ug
Particle 6b-6b:Potential energy U10
Intensity a on potential energyij, document (J.ChemPhys., 107 (11) 4423-4435 (1997)) suggestion identical type
Particle between potential energy intensity aijIt is set to 25.
But the various researchs done later（Such as Macromolcule, volume 39,6744（2006））It is recommended that mutually of the same race
Potential energy intensity a between the particle of classij50 are set to, and the intensity of the potential energy between different types of particle is set to
72。
In this embodiment, with reference to these numerical value, potential energy U1-U10 intensity aijSetting is as follows.
Potential energy U1：aij=72
Potential energy U2：aij=25
Potential energy U3：aij=50
Potential energy U4：aij=72
Potential energy U5：aij=25
Potential energy U6：aij=72
Potential energy U7：aij=50
Potential energy U8：aij=50
Potential energy U9：aij=50
Potential energy U10：aij=50
As described above, polymer mold 5 basic granules 6b through modification and filler model 3 filler particles 4c, 4s it
Between potential energy U2, U5 intensity aij（=25）It is set to be less than the unmodified particle 6a and filler model of polymer beads 6
The intensity a of potential energy U1, U4 between 3 filler particles 4c, 4sij（=72）, therefore, compared with unmodified particle 6a, through repairing
The basic granules 6b of decorations repulsive force reduces.
Affinity increases of this basic granules 6b through modification to filler particles 4c, 4s, therefore can simulate and actually add
The denaturing reagent being added in high polymer material.Therefore, by with this basic granules 6b through modification in polymer mold 5
With reference to the scattered of filler model 3 in polymer mold 5 can be changed, and become that the polymer through modification can be simulated.
In formula（1）In, each potential energy U1-U10 cut-off distance rcIt is defined as foloows.
Potential energy U1：rc=3
Potential energy U2：rc=3
Potential energy U3：rc=3
Potential energy U4：rc=1
Potential energy U5：rc=1
Potential energy U6：rc=1
Potential energy U7：rc=5
Potential energy U8：rc=1
Potential energy U9：rc=1
Potential energy U10：rc=1
According to the present invention, a filler particles 4 of each filler model 3 are defined as the particle 7 of most force.
In addition, following three different cut-off distance rcIt is predefined：
Particle 7 and another filler model 3 of the most force of a filler model 3 most force particle 7 it
Between the maximum cut-off distance that uses；
Any particle 4 and another filler model 3 in a filler model 3 in addition to the most particle 7 of force
In the minimum cut-off distance that uses between any particle 4 in addition to the most particle 7 of force；And
Particle in a filler model 3 most in the particle 7 of force and another filler model 3 except most force
Cut-off distance among being used between any particle 4 beyond 7.
In this embodiment, the center filler particles 4c of each filler model 3 is defined as the particle of most force
7.Therefore, the position between the center filler particles 4c of filler model 3 and the center filler particles 4c of another filler model 3
Energy（Such as U7）The cut-off distance r usedcIt is set to be greater than the surface filler particle 4s and another filler of a filler model 3
Potential energy between the surface filler particle 4s of model 3（Such as U8）The cut-off distance r usedc。
The particle 7 of most force is to end the related filler particles of distance to maximum.Therefore, in filler model 3, come from
Potential energy in the outside of filler model 3, is acting on any other filler particles（Surface filler particle 4s）It is to act on most before
Has the particle 7 of force（Center filler particles 4c）On.Therefore, the particle 7 of most force affects filler model in filler model 3
3 motion.Therefore, in Molecular Dynamics Calculation, representative point that can be by the particle 7 of most force as filler model 3.
If the most mobile increase of the particle 7 of force, then it is assumed that filler model 3 is widely disperseed.
It is desired that as shown in fig. 6, most between the particle 7 and 7 of force（That is center filler particles 4c and 4c it
Between）The big cut-off distance r usedc（Potential energy U7）It is set to be greater than between the particle 4 in addition to the most particle 7 of force
（That is between surface filler particle 4s and 4s）Small cut-off distance rc（Potential energy U8）With above-mentioned spherical surface B radiuses R's and（That is rc+
R）, to ensure before any other filler particles is acted on, potential action is on the particle 7 of most force.
Between the particle 7 of most force, potential energy radial effect.Therefore, in Molecular Dynamics Calculation, computer 1 can
So that filler model 3 to be treated like to the spheroid of practical filling material.
Then, step S3b is carried out, wherein, as shown in fig. 7, the Virtual Space V with predetermined is defined, and fill out
Material model 3 and polymer mold 5 are placed in the V of Virtual Space.
Virtual Space V corresponds to the small component of actual high polymer material, for example as the polymer of analysis target.
In this embodiment, Virtual Space V shape is regular hexahedron, for example the length L1 of each of which side is
20-40[σ].[σ] is long measure.
In Virtual Space, such as, 500-1500 filler model 3 and 1000-3000 polymer mold 5 initially by with
Machine is placed.
Then, simulation steps S4 is carried out.In the step S4, Molecular Dynamics Calculation is carried out.
In Molecular Dynamics Calculation, it is assumed that all filler models 3 and polymer mold 5 in the V of Virtual Space are all deferred to
Classical dynamics, the specific time cycle is calculated according to newton's equation of motion formula, and the time cycle it is each when
Each filler particles 4c, 4s and polymer beads 6a, 6b motion are followed the trail of in intermediate step.
In this embodiment, Molecular Dynamics Calculation is continued, it is artificial until filler model 3 and polymer mold 5
Initial setting up become unartificial setting（Structural relaxation）.
Give one example, the number of intermediate step reached predetermined number at that time（Such as 500-300000）When, molecular dynamics
Calculating terminates.
During Molecular Dynamics Calculation is carried out, the number for all particles being present in system or Virtual Space 8 and
The volume and temperature of system all keep constant.
Then, appraisal procedure S5 is carried out.
In the step S5, according to the result of simulation steps S4 acquisitions, the dispersity of assessment filler model 3.For this
Purpose, step S5a is carried out first.In this step, the mean square displacement of the particle 7 of most force to be assessed is calculated.
Mean square displacement (MSD) is calculated by following formula (2).
MSD=＜ | r (t)-r (0) |2＞ --- (2)
Wherein
R (0) is the coordinate in the center 7c of the particle of most force of specific time point,
The most center 7c of the particle of force coordinate when r (t) is the length t time interval after the time point of feature,
And
＜ ... ＞ represent the particle 7 of predetermined most force and the population mean Jing Guo some time intervals.
In formula (2), | r (t)-r (0) | it is that the particle 7 of most force is advanced during length t time interval
(vector) distance, as shown in Figure 8.
MSD numerical value is obtained, the moving range for grasping the most particle 7 of force can be allowed.
As described above, in Molecular Dynamics Calculation, the particle 7 of most force is treated as the representative point of filler model 3.
Therefore, according to MSD numerical value, the moving range of filler model 3 can be grasped.
The chart for the mean square displacement calculated at some time intervals that Fig. 9 displays are drawn.
Slope θ by regression straight line Lr relative to mean square displacement, the self-diffusion coefficient of the particle 7 of most force can be obtained
(self-diffusion coefficient)
With the raising of self-diffusion coefficient, the moving range of the most particle 7 of force also increases.
Therefore, it is whether big based on self-diffusion coefficient, it can be determined that whether the dispersity of filler model 3 is good.Therefore, can be with
Assess dispersity.
In fig.9, the increase of the mean square displacement of the particle 7 of most force is proportional to the increase of time.This increase meaning
It is big that taste, which moving range, i.e., scattered is good.
In this way, it is not necessary to gauging surface filler particles 4s mean square displacement, it is possible to assess point of filler model 3
The situation of dissipating, and the deployment conditions of filler model 3 are definitely grasped in the short period of time.
For this purpose, it is generally desirable to mean square displacement is calculated at least five time intervals.
In other words, the number of the data of drafting is at least five (in the embodiment that Fig. 9 is shown, 20) number is.
If number is less than five, it is difficult to self-diffusion coefficient is accurately obtained, and may not accurate perception dispersity.
If number is more than 1000, then the calculating time can increase.
Therefore, the preferable scope of the number of time interval is no less than 10 and no more than 100.
Then, step S5b is carried out.In the step S5b, according to obtained mean square displacement whether predetermined acceptable
In the range of, computer 1 judges whether the dispersity of filler model 3 is good.
In this embodiment, if it is determined that the dispersity of filler model 3 is good, then simulation terminates.
On the other hand, if it is determined that dispersity is bad, then consider obtained mean square displacement, change previously in filler model
3 and polymer mold 5 on the condition that sets, and simulated again.This operation is repeated, to find out the quilt of filler model 3
The condition of fine dispersion.
Comparative test
Flow chart according to Fig. 2, Molecular Dynamics Calculation is carried out on filler model and polymer mold.Then,
The mean square displacement of the most particle of force is calculated, that is, calculates the mean square displacement of the center filler particles of filler model.As implementation
Example, as a result shows in Fig. 10.
In addition, the mean square displacement of all filler particles of filler model is calculated, with comparing.As comparative example 1, as a result show
Show in Fig. 10.
In addition, calculate the mean square displacement of all surface filler particles of filler model.As comparative example 2, as a result it is shown in
In Figure 10.
The details of filler model, polymer mold and potential energy is as described above.Other general specifications are as follows.
Each side length L1 of Virtual Space is 30 [σ].
The number of filler model in Virtual Space is 100.
The number of polymer mold in Virtual Space is 1500.
The number of the time step of Molecular Dynamics Calculation is 100000.
Mean square displacement is calculated at the time interval of 20 times.
In addition, without using the position of the filler particles obtained in above-mentioned Molecular Dynamics Calculation, respective filler mould is calculated
The position of the gravity station of type, and calculate the mean square displacement of gravity station.（As the experimental example in table 1）
Then, according to mean square displacement, embodiment, comparative example 1, comparative example 2 and experimental example are compared.As a result such as table 1
It is shown.
Then, on calculating the time, embodiment, comparative example 1, comparative example 2 and experimental example are compared.As a result such as table 1
It is shown.
Table 1
| Method | Experimental example | Embodiment | Comparative example 1 | Comparative example 2 |
| Mean square displacement | 1.08 | 1.05 | 3.01 | 3.48 |
| Calculate the time (hour) | 9.90 | 1.10 | 9.88 | 8.75 |
According to the comparison of mean square displacement, it was confirmed that embodiment can simulate the filler dispersity close to experimental example, therefore,
Can reliably it be assessed.
In addition, in embodiment, it is not necessary that the gravity station in experiment with computing example, it is therefore apparent that when reducing calculating
Between.
Claims (4)
1. a kind of computerization analogy method for being used to assess that filler is scattered in high polymer material, including：
The filler model of filler is defined, wherein each filler model represents multiple filler particles, the multiple filler particles are single
The particle and at least four surface particles of individual most force, the surface particles are centrally located on spherical surface, described spherical
The center on surface and the center superposition of the particle of the single most force；
The polymer mold of high polymer material is defined, wherein each polymer mold represents one or more polymer beads；
Potential energy between definitions particles, the particle are filler particles and polymer beads, wherein,
Each potential energy is the function of the distance between granular center and is defined as being reduced to predetermined cut-off in the distance
Apart from it is following when to interact between particle,
End distance for the particle definition maximum of the single most force, and
The cut-off distance less than the maximum cut-off distance is defined for each surface particles；
In each filler model, the equilibrium length between the particle of single most force and each surface particles is defined；
In each filler model, the equilibrium length between surface particles is defined；
Molecular Dynamics Calculation is carried out to the polymer mold and filler model being placed in predetermined Virtual Space；And
According to the dispersity of the outcome evaluation filler model obtained by Molecular Dynamics Calculation,
Wherein
By calculate the single most force particle mean square displacement without calculate the mean square displacement of each surface particles come
The mean square displacement of each filler model is obtained, and
The dispersity of filler model is assessed according to the mean square displacement of the filler model obtained, wherein
Between the particle of single most force in two filler models cut-off distance be more than the spherical surface radius and
The sum of cut-off distance between the surface particles of two filler models, wherein,
Potential energy between definitions particles includes：
Between the particle of most force and the particle of the most force in another filler model in one filler model of definition
Maximum cut-off distance；
Define in a filler model any particle in addition to the most particle of force with another filler model except
Minimum cut-off distance between any particle most outside the particle of force；And
Define in a filler model in the most particle of force and another filler model in addition to the most particle of force
Any particle between among cut-off distance.
2. analogy method as claimed in claim 1, it is characterised in that
Mean square displacement is calculated at time interval more than five times.
3. analogy method as claimed in claim 1, it is characterised in that
The function of potential energy is shown below between definitions particles：
U=aij(1-rij/rc)2/2
In formula,
U is potential energy,
aijThe constant of potential energy U intensity is corresponded to,
rijIt is the distance between center of the particle, and
rcIt is the cut-off distance between the particle.
4. analogy method as claimed in claim 3, it is characterised in that
Assessing dispersity includes obtaining the self-diffusion coefficient of the most particle of force.
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| JP2012112678A JP5466727B2 (en) | 2012-05-16 | 2012-05-16 | Method for simulating polymer materials |
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| JP5602190B2 (en) * | 2012-06-08 | 2014-10-08 | 住友ゴム工業株式会社 | Method for simulating polymer materials |
| US20140067350A1 (en) * | 2012-08-31 | 2014-03-06 | Sumitomo Rubber Industries, Ltd. | Method for simulating polymer material |
| CN103678814B (en) * | 2013-12-18 | 2016-06-29 | 北京航空航天大学 | The eccentricity prebias method for designing of critical inclination near-circular orbit |
| CN103853887B (en) * | 2014-03-05 | 2016-09-14 | 北京航空航天大学 | The satellite orbit of the eccentricity of a kind of Frozen Orbit determines method |
| JP6360392B2 (en) * | 2014-09-04 | 2018-07-18 | 住友ゴム工業株式会社 | Method for simulating polymer materials |
| JP6408874B2 (en) * | 2014-11-14 | 2018-10-17 | 住友ゴム工業株式会社 | Method for simulating modified polymer materials |
| JP6050903B1 (en) * | 2016-01-22 | 2016-12-21 | 住友ゴム工業株式会社 | Method for simulating polymer materials |
| JP6891548B2 (en) * | 2017-03-08 | 2021-06-18 | 横浜ゴム株式会社 | Composite material analysis model creation method, composite material analysis model creation computer program, composite material analysis method and composite material analysis computer program |
| CN109580431B (en) * | 2019-01-28 | 2021-06-29 | 贵州电网有限责任公司 | SF (sulfur hexafluoride)6/N2Method for determining diffusion characteristics of mixed gas |
| CN114664390B (en) * | 2022-05-23 | 2022-09-13 | 苏州创腾软件有限公司 | Method and system for generating cross-linked polymer space network structure in simulation mode |
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| US20130311155A1 (en) | 2013-11-21 |
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| CN103425815A (en) | 2013-12-04 |
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